Basic Principles of Homing Guidance - The Johns Hopkins ...

BASIC PRINCIPLES OF HOMING GUIDANCENoiseLOSSeeker++ + + – – Gimbal angle1/s 1/sReceiver1LOS rate pickoff m 1 s .cLOS rate estimate^1 . f s + 1Guidance PNfilterGuidance computera McCommandedaccelerationNV cG FC (s).++Gimbal servoDish rateGimbal controlRate gyro1 .+–Flight controlsystem.Body attitude ratea A s + 1v mAchievedaccelerationBody rateaerodynamicsFigure 5. Simplified planar model of a traditional LOS rate reconstruction approach that directly supplies an LOS rate measurementto the guidance computer. Note that the LOS rate pickoff is assumed to be proportional to the boresight errormeasurement. The measured LOS rate is subsequently filtered to mitigate measurement noise and then applied to the PNhoming guidance law.Moreover, the transfer function from commanded acceleration(from the guidance law) to missile body rate (ċ)is approximated by the following aerodynamic transferfunction, where t Ais the turning rate time constant andv mis missile velocity:o A s + 1= .a vcm(26)In this approach, the fact that the LOS rate is embeddedin the tracking error ( m) is exploited. As illustrated, aLOS rate estimate is derived by appropriately filteringthe receiver tracking error scaled by the seeker tracklooptime constant.Other approaches can be used to derive LOS rate forhoming guidance purposes; these are generally referredto as either LOS reconstruction or LOS rate reconstruction.We next outline three alternative techniques (twoLOS reconstructions and one LOS rate reconstruction).LOS ReconstructionAs shown in Fig. 3, LOS reconstruction works toconstruct a measured LOS, l m, in an inertial frame ofreference. The measured LOS then is filtered (via anappropriate guidance filter) to derive an estimate of LOSrate for guidance purposes. Two different LOS reconstructionapproaches are as follows: 91. Integrate the seeker gyro output and sum it with themeasured tracking error. A block diagram of thisapproach is shown in Fig. 6. Mathematically, thisapproach can be expressed as Eq. 27:l m= m+ # . dt . (27)2. Integrate the output of the missile body rate gyro,obtained from the missile IMU, and sum the integratedIMU gyro output together with the seekergimbal angle and the measured tracking error. Weillustrate this approach in the block diagram shownin Fig. 7. This approach is expressed mathematicallyas shown in Eq. 28:l m= m+ b + # ċ dt . (28)From Fig. 3, it is clear that the two concepts are algebraicallyequivalent in the absence of noise and assumingperfect instruments (no gyro biases, drift, etc.); however,in practice, this is not the case. Moreover, we note that,in general, the guidance filters for the two approachesare not necessarily the same (e.g., for the simplified guidancefilters shown in the figures, the filter time constants,represented by t f, are not necessarily the same).The fundamentals of guidance filtering will be discussedin the companion article in this issue “Guidance FilterFundamentals.” It is shown in Ref. 9 that the two LOSreconstruction approaches can yield significantly differentresults when noise and imperfect instrumentsare used. How these differences manifest themselvesdepends on the quality of the measurements and instrumentsthat are used.LOS Rate ReconstructionA guidance signal also can be generated by differentiatingthe tracking error and adding it tothe seeker rate gyro output. For practical purposes,taking the derivative of the tracking error is accom-JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 29, NUMBER 1 (2010)31­